Numerical work with sagemath 25: The Wigner D matrix

This week I have been studying the paper ‘A New Realisation of Quantum Geometry’. I’ll review the paper in the next post and follow up that with an analysis of the area operator in  the SU(2) case.

What I’m posting at the moment is some exploratory work looking at the behaviour of the Wigner D matrix elements and U(1)area operator using python and sagemath.

Below I look at the general behaviour of the Wigner D matrix elements:

code1

graph1

Below  Here I  look at the behaviour of the spectrum of the area operator with U(1).

code2

graph2

Below I look at the how the area varies with μ for the values 0.1, 0.3, 0.5:

code3

graph3

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